US6081820A - Method and apparatus for filtering a signal using a window value - Google Patents
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- US6081820A US6081820A US09/026,860 US2686098A US6081820A US 6081820 A US6081820 A US 6081820A US 2686098 A US2686098 A US 2686098A US 6081820 A US6081820 A US 6081820A
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0248—Filters characterised by a particular frequency response or filtering method
- H03H17/0261—Non linear filters
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- This invention relates to apparatus and methods for filtering a signal, and, more particularly, to an efficient filtering apparatus and method wherein the output of the filter is kept constant until the difference between the signal and the previous output of the filter is greater than a window value.
- a filter is basically a system or method that selectively changes the waveshape, amplitude-frequency and/or phase-frequency characteristics of a signal in a desired manner.
- filters include highpass filters, polar filters, and Butterworth filters, and can involve a number of analog electronic circuits as well as mathematical models and techniques, such as Fourier transformations.
- a digital filter refers to hardware or software that performs a mathematical algorithm that operates on the digital input signal to produce a digital output signal for the purpose of achieving a filtering objective.
- ADC analog-to-digital convertor
- the digital filter implements the filtering operation in accordance with the computational algorithm for the filter.
- a digital-to-analog convertor or DAC
- While digital filters can be very beneficial in digital signal processing, they are not without limitations. Such filters can be extremely complex. Typically, the input and output signals of such filters are related by complex difference equations that include convolution sums. Although computer software and/or hardware are utilized to solve these complex equations, the use of such filtering algorithms requires the computer to make a number of mathematical calculations per filtering cycle, and also requires a sizable amount of data storage capacity for storing the filter coefficients and filter data. Of similar complexity is the design of the appropriate digital filter, which requires the computation of filter coefficients by using particular methods, such as the impulse invariant method or bilinear transformation method, and the realization of the filter into a suitable structure, such as a lattice structure or cascade structure.
- At least one less complex filtering method has been developed. According to the method, anytime the input number is greater than a predetermined range, the input number would be provided as the output of the filter, and the range would be shifted to the right such that the input number would become the upper "edge" of the range (i.e., the highest number in the range). Similarly, anytime the input number would be less than the range, the input number would be provided as the output, and the range would be shifted left such that the input number would become the lower "edge” of the range (i.e., the lowest number in the range). However, whenever the input number fell within the range, the input number would not be output, and, rather, the last number output from the routine would be provided as the filter output.
- the first method does not adequately suppress increases or spikes in the signal. Whenever a spike occurs that falls outside of the window range, the range will shift right (i.e., toward the positive direction) and that spike will become the upper "edge" of the range. However, any additional noise that is greater in amplitude than that edge will not be suppressed, and even a slight upward drift in the signal that happens to be greater than the spike would not be stabilized by the method. Due to this effect, instability and imprecision in the filter output can result. The same is true for any low points or lulls in the signal.
- the first low point that falls outside of the range would cause the range to shift left (i.e., toward the negative direction), and the low point would become the lower "edge" of the new range.
- any future low points that fall below this edge such as can be caused by a drift in the signal, would not be stabilized by the method.
- the "shift and add" layer of filtering can lead to imprecision and inaccuracy, as the truncating of the least significant bits can create large errors in the signal. While the precision can be increased by increasing the number of samples added, this solution slows the process significantly.
- Another object of the present invention is to provide a method and apparatus for filtering a signal that can be implemented, preferably in hardware and/or software, with a relatively small amount of equipment, code, and cost.
- a further object of the present invention is to provide a method and apparatus for filtering a signal that, in comparison to conventional filters, can operate at higher speeds, and require fewer computations, and less processing time, and memory.
- Another object is to provide a filter which provides increased stability, even in the presence of signal spikes and drifts in the incoming signal.
- An additional object is to provide a filter which provides increased precision and accuracy.
- a method for filtering a signal comprising the steps of obtaining an input, obtaining a previous output, determining a relationship between the previous output, the input, and a window value, and providing an output based upon the relationship.
- the input corresponds to a portion of the output of the device.
- the output is equal to the previous output if the input is within a range of deviation, and the output is equal to the input if the input is outside of the range.
- the range of deviation is at least partially defined by the window value and includes a lower limit and an upper limit, the previous output being less than the upper limit and greater than the lower limit.
- the window value completely defines whether the input sample is sufficiently close or sufficiently different from the previous output (or other reference that may be utilized). It is also preferred that the relationship determination is made by comparing the window value to the difference between the reference sample (such as the previous output) and the input sample, and the output sample is set equal to the reference sample when the window value is greater than the difference, and set equal to the input sample when the window value is less than the difference.
- the reference sample such as the previous output
- an apparatus for stabilizing the output of a device comprising an output storage element for providing a stored output signal, and an evaluation element.
- the evaluation element receives a window signal, a device output signal corresponding to the output of the device, and the stored output signal, and provides an output signal.
- the output of the evaluation element is equivalent to the device output signal when the difference between the device output signal and the stored output signal is greater than the window signal.
- the output of the evaluation element is equivalent to the stored output signal when the difference between the device output signal and the stored output signal is less than the window signal.
- the evaluation element comprises a pair of comparators, an adder, a subtractor, and a logic element. It is also preferred that the stored output signal is equal to the previous output of the apparatus.
- FIG. 1 is a schematic view of an environment in which the method and apparatus, of the present invention can be practiced
- FIG. 2 is a flow diagram illustrating a method for filtering a signal using a window value, according to one embodiment of this invention
- FIG. 3 is a flow diagram illustrating another embodiment of the present invention in which dual layers of filtering are utilized, one of the layers being similar to the method illustrated in the diagram of FIG. 2;
- FIG. 4 is a block diagram showing an apparatus for filtering a signal using a window value input.
- FIG. 1 illustrates a preferred environment in which the window filter 16 of the present invention may be applied.
- an analog signal is received at input 10 and filtered in the desired manner by analog filter 12.
- the output of the analog filter 12 is fed to an analog-to-digital convertor 14, which samples the analog input and converts it into digital form.
- a first digital filter 15 can then be utilized to provide a first layer of digital filtering to the digital signal output from the ADC 14.
- the digital signal is fed to a second digital filter 16, which comprises an embodiment of the present invention.
- the output of the filter 16 is then ready for processing by a digital processor 18, which may apply any of a number of digital signal processing algorithms and/or computations to the signal.
- the signal can then be fed to a digital-to-analog convertor 20, which is utilized to convert the digital signal into an analog form, and then to another analog filter 22 for final filtering.
- the output of the analog filter 22 is provided at output 24.
- the apparatus and method of the present invention be used to filter and stabilize a digital signal, such as through the use of digital filter 16 of FIG. 1, the invention may be used to filter other signals as well.
- the signal may already be in digital form, in which case filter 12 and ADC 14 would not be needed.
- the digital output of filter 18 may not need to be converted to analog form (such as, for example, if the signal is to be stored in computer memory for later use, or displayed on a display device), in which case DAC 20 and analog filter 22 would not be needed.
- the window filter 16 may be utilized as the sole means of filtering, and, accordingly, does not need to be used in conjunction with other filters.
- the filter and filtering method of the present invention may be utilized in a number of machines, devices, and processes.
- the present invention may be utilized to process signals in industrial machines, such as feedback signals fed to PID controls in injection molding machines, machine tools, and the like, or to process signals in consumer items, such as the audio signals in radios and CD players.
- the filter may also be used to smooth or stabilize data obtained from a variety of processes and devices.
- the invention may take on a number of forms, such as, for example, computer software and/or hardware, along with other electrical and digital devices.
- FIG. 2 is a flow diagram illustrating one embodiment of the filtering method of the present invention.
- the method according to this invention can be embodied as an article of manufacture by configuring the method as a program on a computer readable medium, such as a floppy disk, CD-ROM or other persistent storage medium.
- the method can also be embodied as a special purpose apparatus having executable instructions suitable for carrying out the invention stored in a RAM or ROM, or a combination of both.
- the method can be implemented in any conventional programming language, such as, for example, C, C++, or Basic, or can be implemented in a special purpose programming language.
- the program is implemented in C programming language.
- block 30 Upon execution of the method of FIG. 2, block 30 is executed and the size of the "window" utilized in the filter is obtained.
- This window comprises a signal, sample, variable, or constant having a particular value.
- the larger the value of the window the more noise that is suppressed by the method, and the more stable the output of the filter.
- a large window value also means that the output of the method will have less resolution and accuracy.
- the value of the window can be obtained from the user of the method, from a separate software routine or data location, or from another signal source.
- a sample of the signal to be filtered is obtained, or input.
- the signal to be filtered is a digital signal, as in a preferred embodiment, this sample comprises a data value, or word, that has a particular magnitude and that is represented by a number of bits, as known in the art.
- a plurality of such samples represent the digital signal itself, and the digital signal represents an analog signal sampled at discrete moments in time.
- the sample may represent and take the form of other signals and/or values as well.
- the sample received at block 32 can be loaded directly from an ADC, from a database having such samples stored therein, or from some other signal source. It is this sample upon which the method will operate, and, thus, the sample can be referred to as the input sample.
- the previous output of the method represents the output of the method during the iteration of the method preceding the present iteration, and is used as a reference signal or reference sample for the method.
- This previous output can be stored in a memory location or data base and can be represented by a data array or variable, as in FIG. 2, wherein it is represented by the variable "last output.”
- the variable can be assigned a predetermined value, such as a random value.
- the variable can take on the number that currently resides in the storage register for the variable.
- blocks 34 and 36 can be skipped, and blocks 38, 42, and 44 can be executed, which will simply allow the input sample to be output and will set the variable "last output" equal to the input sample.
- the absolute value of the difference between the sample and the last output is determined, as it is the magnitude of this difference that is of importance to the method. Also, by taking the absolute value, it is ensured that the last output (or reference sample) is disposed at the center of the window, or range of deviation (i.e., that stability is provided in both the positive and negative directions).
- the difference between the sample and the last filter output is compared to the window value that was input at block 30. If the difference is greater than the window value, then block 38 is executed wherein the variable "filter output" is set equal to the sample which was input at block 32. If this difference is less than or equal to the window value, then block 40 is executed wherein the "filter output” is set equal to the variable "last output”. It is to be understood that other relationships between the sample, the window value, and the last filter output can be determined at blocks 34 and 36 without departing from the scope of the invention. Any method of determining whether the sample is sufficiently close to the last output is within the scope of the present invention.
- One way to so is to multiply the last output by a constant value and determine whether the input sample is greater and/or less than the result of the multiplication. As illustrated at blocks 34 and 36, a preferred method is to determine if the input sample exceeds the last output (i.e., the reference sample) by more than the predetermined window value.
- the filter output may be set equal to the input sample when the difference equals the window value, without departing from the scope of the invention.
- the "filter output" variable is provided (or output) so that it may be used or analyzed, such as, for example, by displaying the value of the variable on a memory device, by providing the value as a signal on an output port, or by allowing the variable to be used by a user or another program.
- Block 44 is then executed wherein the variable "last output” is set equal to the variable "filter output", so that it may be used during the next iteration of the method. After block 44, this next iteration is commenced and the next sample to be processed is obtained at block 32 (i.e., after block 44, the process returns to block 32 for operation on the next sample or signal).
- this embodiment of the present invention maintains a constant output signal until the difference between a particular input sample and the constant output signal is greater than the window value, at which time the output will change, preferably to equal that particular input sample.
- the method is reiterated on subsequent samples and this new output will be maintained until an input sample is encountered that falls outside of the "window", or range.
- the variable "last output" which represents the previous output of the method, serves as a reference to which each sample is compared.
- other references may be used without departing from the scope of the invention
- the filter will provide 30 as its output until a sample is obtained that is greater than 40 or less than 20.
- the filter makes 19 its new output and maintains this output until a sample is encountered that is greater than 29 or less than 9.
- these numbers would be provided in binary or hexadecimal form in practice. This example is depicted by the following table:
- the method of the present invention may also be utilized with other filtering or signal processing methods, such that additional layers of error correction and stability are provided.
- the flow diagram of FIG. 3 depicts such "dual filtering", wherein blocks 54, 56, and 58 relate to a first method of filtering, which utilizes a moving average, while blocks 60, 62, 64, and 66 relate to a second method of filtering, which utilizes another embodiment of the method of FIG. 2.
- the window value and number of samples are obtained, the window value being used in the second layer of filtering and the number of samples "n" being utilized in the first layer.
- the window value is used in the same manner as described in FIG. 2, and the value of "n” determines the number of samples that will be combined with the current sample to calculate an average value. Both values can be set by a user according to the desired characteristics of the filter.
- the sample to be filtered or processed by the method is obtained.
- the sum of the input sample and the previous samples is obtained.
- the number of previous samples that are included in the sum is determined by the value "n" input at block 50.
- the sum is then used at block 56 to calculate an average (which, in FIG. 3, is assigned as the variable "average"), the average being equal to the sum divided by (n+1).
- the input sample is saved, preferably in an array, for use in averaging other input samples during other iterations of the method.
- blocks 54, 56, and 58 correspond to a "moving average" type of filter that can be used in conjunction with the filter depicted in FIG. 2.
- this filtering method can be modified such that samples that were received previously and subsequently are used in calculating the average.
- a circular averaging technique can be utilized, by utilizing a circular buffer which contains values received both before and after the sample input at block 52, the number of values stored in the buffer being determined by the number "n" which is input at block 50.
- a linear buffer or finite buffer may be utilized.
- the output of the first filter is then fed through a second filter, represented by blocks 60, 62, 64, and 66, so that a second layer of filtering is provided.
- a second filter represented by blocks 60, 62, 64, and 66.
- These blocks illustrate one alternative to the embodiment illustrated in FIG. 2.
- the variable "average”, calculated from the first filtering layer is compared to a sum, the sum being equal to the last output of the dual filter, indicated in the drawing as the variable "last average", plus the window value.
- the average is compared to a difference, the difference being equal to the last output of the method minus the window value.
- block 64 is executed wherein the variable "last average” is set equal to the variable "average", which is then output, at block 68.
- block 66 is executed wherein the variable "average” is changed to be equal to the variable "last average.” The variable "average” is then output at block 68, and the method returns to block 52 where the next sample to be processed is obtained.
- the method of blocks 60, 62, 64, 66, and 68 produce the same effect as the method depicted in FIG. 2.
- the method is reiterative, and the output of the method is held constant until the average calculated in the first filtering layer differs from this constant output by a certain value, which is determined by the window value. At this time, the output is changed to equal the average calculated by the first layer.
- the only differences between the window filtering methods of FIG. 2 and FIG. 3 is that two comparisons are used in FIG. 3 (which in combination are equivalent to the one comparison of FIG. 2) and the manipulation and outputting of variables is slightly different. The effect of the two are identical.
- the reference i.e., the last output
- the window value helps determine a range of deviation having a lower limit and an upper limit and which has the reference as the approximate center.
- the reference is output whenever the input is between the two limits (i.e., when the input is within the range of deviation); otherwise, the input is provided as the output (i.e., when the input is outside of the range of deviation).
- the limits may be defined by substraction and/or addition, as described in the methods of FIG. 2 and FIG. 3. Alternatively, it is contemplated that the limits may be defined by other calculations, such as, for example, multiplying the reference by a constant and/or constants.
- the method of the present invention may be combined with other filtering methods and/or signal processing techniques.
- the outputs of the filtering methods can be tapped at 46 in FIG. 2 and 70 in FIG. 3, and can be utilized for a number of purposes in a wide variety of applications.
- FIG. 2 and FIG. 3 are preferably embodied in computer programs that utilize input statements, output statements, decision statements, assignment statements, loops, variables, arrays, and/or other statements and techniques.
- such programs may take on a number of forms, utilize a variety of variable names and commands, and be implemented in any of a number of programming languages without departing from the scope of the invention.
- the steps of the method of the present invention may be practiced in a number of orders, without departing from the scope of the invention.
- FIG. 4 depicts a preferred hardware embodiment of the present invention.
- the signal to be stabilized or filtered by the device is provided at input 100.
- This signal is fed to a pair of comparators, 102 and 104, each of which is also provided with a reference signal.
- Comparator 102 is provided with a maximum reference signal at input 103 while comparator 104 is provided with a minimum reference signal at input 105.
- the maximum reference signal provided to comparator 102 is provided by an adder 106 to which is fed a predetermined window signal, provided on line 107, and the output of a storage device 110.
- the minimum reference signal provided to comparator 104 is provided by a subtractor 108 to which is fed the predetermined window signal on line 107, and the output of the storage device 110.
- the adder 106 can comprise any adder known in the art, such as a binary full adder.
- the comparators 102 and 104 can comprise any device known in the art to be useful for comparing two values or signals, and the subtractor 108 can comprise any device suitable for subtracting two values.
- the outputs of the comparators are fed to a logic device 112, which provides an output depending upon the outputs of the comparators 102 and 104.
- the logic device may comprise an application specific integrated circuit, field programmable gate array, or other apparatus useful for performing logic operations.
- the storage device 110 is connected to the logic device 112 for storing each output of the logic device for later use, and can comprise any memory element well known in the art, such as a CMOS random access memory chip (RAM).
- the electronic adder 106 adds the predetermined window signal to the previous output of the logic element 112, which is stored in storage device 110, and provides the maximum reference signal at its output.
- the electronic subtractor 108 subtracts the window signal from the previous output of the logic element 112, and provides the minimum reference signal at its output.
- the comparator 102 compares the magnitude of the maximum reference signal to the magnitude of the signal to be filtered, illustrated in FIG. 4 as x, and provides an output, which is either in a first state (e.g., a "high” state or logical 1), if the maximum reference signal is greater than x, or a second state (e.g., a "low” state or logical 0), if the maximum reference signal is less than x.
- the comparator 104 compares the magnitude of the minimum reference signal to the magnitude of the signal x and provides an output which is in a first state if the minimum reference signal is greater than the signal x, and a second state if the minimum reference signal is less than x.
- the logic device 112 is configured with control logic such that the device will provide an output that is dependent on the outputs of the comparators 102 and 104. If the signal x is less than the maximum reference signal and greater than the minimum reference signal, as indicated by the states of the comparators 102 and 104, the logic device 112 will output its previous output, which is stored in storage device 110. If the signal x is either greater than the maximum reference signal or less than the minimum reference signal, as indicated by the comparators 102 and 104, the logic device 112 will output the signal x as its output. Every output of the logic device 112 is stored in the storage device 110 for use during the next cycle by the adder 106, subtractor 108, and logic device 112.
- the apparatus of FIG. 4 stabilizes the input signal by providing an output that is constant until an input signal is encountered which varies from the output by an amount that is greater than the window signal, at which time the new input signal becomes the output and the cycle is repeated.
- the window signal can be provided by the user or obtained from a memory device or other signal source. As in the method of FIG. 2, the larger the size of the window signal, the more stability provided, at the cost of less accuracy and resolution.
- FIG. 4 depicts one hardware embodiment of the present invention, other embodiments are possible without departing from the scope of the invention.
- the functioning of several of the devices described herein may be combined or otherwise consolidated into one device.
- each device depicted in FIG. 4 may comprise a number of electronic devices and circuits known in the art.
- the present invention provides a signal processor that can effectively correct errors in a signal, eliminate noise and distortion in a signal, and otherwise filter and stabilize the signal, without the complexities of design and operation associated with prior devices and methods. Moreover, the present invention minimizes necessary hardware, reduces processing time, and is easily adaptable to a variety of applications. In addition, the invention provides greater stability and precision than other filters known in the art.
Abstract
Description
______________________________________ Time Sample Obtained (e.g. from ADC) Output of Method ______________________________________T1 30 30 T2 28 30T3 24 30 T4 29 30T5 22 30 T6 23 30 T7 19 19T8 20 19T9 22 19 T10 23 19 ______________________________________
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